Hey Nick,
I'm really sorry you didnt' get any help in the forums, a lot of people are currently upset with the game so we dont' have the best mindset in here.
The one time the game went on it seemed whatever i did the computer had got much better stuff and way more stuff and it was just a matter of time then.
* There is currently an issue where the AI can go into the negatives for his economy (Gold for example) and when he does so. He just keeps digging deeper. So in that aspect the AI can build up and train units without ever worring about upkeep.
* Also, there is another issue with the Warrior Temple (maybe wrong name) where it causes the AI to be able to build any unit in...1 turn.
These 2 points combined will really mess with your games. So it's basically because of this you are seeing he AI suddenly starts spiking in military power.
I have to say that, although I sympatize with your situation, i'm a little jealous. In my games the AI will build up, and then... just start building units and start sending them around with no specific idea in mind. I just kills me inside. I had all the factions Declare war on me once, and after passing 100 turns... still no armies in sight... Uh? (And this also happens to factions that I have communal borders with)
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Suggestions:
I've seen a lot of people state that the "easy" setting ends up being hard. Maybe it's because with easy difficulty the AI dosen't have all his economic boosts, so his chances of falling in the negative are stronger and thus he gets into his infinite resource status faster. (This would be "funny")
I would suggest playing games with Large Maps, Epic Pacing, and take like 3-4 oponents max. If you want less chance of a conflict pick Empire Factions as you will get a slower decrease to your relations as you are of the same allegiance.
Playing on Large Map with 3-4 oponents will MOST LIKELY give you a lot of space to start with, and no need to be worried about starting next to another faction. Take note that there are 'minor' factions. So when you see a border with a color that is not consistent with any of the chosen factions, it's one of these minor factions. Which "should" be a pushover, so feel free to conquer/attack those a little more early on.
If you can get the Leather armor tech, with the Team ability. You can make a full leather armor troop armed with a spear or staff, and it will have a lot of defense when in your cities and should provide at least deterrent for the enemy to attack.
If that dosen't help, tell me the outcome and i'll try to help you out some more.
Hope it helps!
Cheers,
V